The LHCb Collaboration has recently reported the discovery of direct CP violation in combined $D^0 \to K^+ K^-$ and $D^0 \to \pi^+ \pi^-$ decay modes at the $5.3 \sigma$ level. Assuming U-spin symmetry (i.e., $d \leftrightarrow s$ interchange symmetry) for the strong-interaction parts of these two channels, we find that their corresponding direct CP-violating asymmetries are ${ \cal A}^{ }_{ \rm CP} (K^+ K^-) \simeq \left(-7.7 \pm 1.5\right) \times 10^{ -4}$ and ${ \cal A}^{ }_{ \rm CP} (\pi^+ \pi^-) \simeq \left(7.7 \pm 1.5\right) \times 10^{ -4}$. The CP-forbidden transition $e^+ e^- \to D^0\bar{ D}^0 \to \left(K^+ K^-\right)^{ }_D \left(\pi^+ \pi^-\right)^{ }_D$ on the $\psi(3770)$ resonance is therefore expected to have a rate of ${ \cal O}(10^{ -10})$ or smaller under U-spin symmetry, and it can be observed at a high-luminosity super-$\tau$-charm factory if at least $10^{ 10}$ pairs of coherent $D^0$ and $\bar{ D}^0$ events are accumulated.
Categories: hep-ph